-
Notifications
You must be signed in to change notification settings - Fork 7
/
congo.html
159 lines (147 loc) · 7.74 KB
/
congo.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
<!DOCTYPE html>
<html>
<head>
<link href="https://fonts.googleapis.com/css?family=Raleway" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Merriweather" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Anton" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Lobster" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Abel" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Monoton" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Roboto+Mono" rel="stylesheet">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
<link rel="stylesheet" href="https://www.w3schools.com/w3css/4/w3.css">
<!-- TITLE AND CUSTOM CSS -->
<title> Congruency Modulo</title>
<link rel="stylesheet" href="css/cony.css">
</head>
<body>
<script>
function openNav() {
document.getElementById("mySidenav").style.width = "15%";
}
function closeNav() {
document.getElementById("mySidenav").style.width = "0";
}
</script>
<div class="header">
<h1 style="color: white"><b>Number Theory</b></h1>
<p style="color: white">Theory Of Numbers</p>
</div>
<div class="topnav">
<div id="mySidenav" class="sidenav">
<a href="javascript:void(0)" class="closebtn" onclick="closeNav()">←</a>
<a href="https://www.amazon.com/s/ref=nb_sb_noss_2/144-7551219-7280505?url=search-alias%3Daps&field-keywords=number+theory">Shop</a>
<a href='#'>Books</a>
<a href='Devs.html'>Developers</a>
<a href='#' id="feed">Feedback</a>
</div><a style="font-size:20px;cursor:pointer ;color:white ; padding-bottom: 8px" onclick="openNav()">☰</a>
<a href="index.html">Home</a>
<div class="dropdown">
<button class="dropbtn">
Primes
<!--<i class="fa fa-caret-down"></i>-->
</button>
<div class="dropdown-content">
<a href="Primality.html">Introduction</a>
<a href="PrimeFact.html">Prime Factors</a>
<a href="RSA.html">RSA Encryption</a>
</div>
</div>
<div class="dropdown">
<button class="dropbtn">
Modular Arithmetic
<!--<i class="fa fa-caret-down"></i>-->
</button>
<div class="dropdown-content">
<a href="welcome.html">Introduction</a>
<a href="ModularAddMulSub.html">Modular Arithmetic</a>
<a href="congo.html">Modular Congruency</a>
</div>
</div>
<div class="dropdown">
<button class="dropbtn">
Algorithms
<!--<i class="fa fa-caret-down"></i>-->
</button>
<div class="dropdown-content">
<a href="bubble.html">Bubble Sort</a>
</div>
</div>
</div>
<div class="w3-container">
<button class="w3-button w3-xlarge w3-circle w3-red w3-card-4" id="myBtn">+</button>
</div>
<!-- CONTENT -->
<div id="myModal" class="modal">
<!-- Modal content -->
<div class="modal-content">
<textarea rows="6" cols="50" placeholder="Give your reviews..." style="color:black"></textarea>
<span class="close">×</span>
<button class="button" type="button" onclick="submit()" style="height:45px;width:200px ;padding:10px;font-size: 18px"><span>Submit</span></button>
</div>
</div>
<div class="row">
<div class="leftcolumn">
<div class="card">
<h2><span style="margin-left: 300px"><b>Congruence Modulo</b></span></h2>
<h3 style="font-family: Raleway">Introduction To Congruence Modulo</h3>
<p style="font-size: 18px">You may see an expression like:
<br><span style="margin-left: 350px"><b><i>A≡B(mod C)</i></b></span>
<br>This says that A is congruent to B <b><i>mod</i></b> C.
<br>
</p>
<p> We will discuss the meaning of congruence modulo by performing a thought experiment with the regular modulo operator.</p>
<p>Let's imagine we were calculating mod 5 for all of the integers:</p>
<h2 style="font-family: Merriweather">Examples With Visualisation</h2>
<br>
<div style="margin-left: 65px"><img src='css//img///congo.png'></div>
<br>
<p style="font-size: 18px">Suppose we labelled 5 slices 0, 1, 2, 3, 4.</p>
<p>Then, for each of the integers, we put it into a slice that matched the value of the integer mod 5. Think of these slices as buckets, which hold a set of numbers. For example, 26 would go in the slice labelled 1,</p>
<p>because <b><i>26</i> mod <i>5</i></b> = <b><i>1</i></b> Above is a figure that shows some integers that we would find in each of the slices. </p>
<p style="font-size: 18px"> It would be useful to have a way of expressing that numbers belonged in the <b>same slice.</b>
<br>(Notice 26 is in the same slice as 1, 6, 11, 16, 21 in above example)
<p>A common way of expressing that two values are in the same slice, is to say they are in the same equivalence class.
<br> The way we express this mathematically for mod C is:<b> A≡B (mod C)</b></p>
<p>In plain English, the above statement says "A is congruent to B modulo C."</p>
<p>Examining the expression closer:</p>
<p><b>1.</b> ≡ is the symbol for congruence, which means the values A and B are in the same equivalence class.</p>
<p><b>2.</b> The (mod C) within the parenthesis tells us what operation we applied to A and B.</p>
<p><b>3.</b> When we have both of these, we call "≡" congruence modulo C.</p>
<p style="padding-left: 800px;font-size: 10px"><i>Source : KhanAcademy.com</i></p>
</div>
<div class="card">
<h2>Congruency Tester</h2>
<br>
<br>
<div style="margin-left: 250px">
<form>
<input type="number" id="data1" placeholder="A" required>
<input type="number" id="data2" placeholder="B" required>
<input type="number" id="data3" placeholder="C" required>
</form>
<br>
<p>
<button style="margin-left: 50px" class="button" onclick="congoMod()">Get Mod</button>
<p id="ans" style="font-family: Merriweather;margin-left: 60px"><b></b></p>
</div>
</div>
</div>
<div class="sticky">
<div class="card">
<h2 style="font-family: Merriweather">References</h2>
<div>
<a href="https://ocw.mit.edu/courses/mathematics/18-785-number-theory-i-fall-2016/"><img src="css//img//mitocw_1024x768.jpg" alt="mitocw" style="height: 200px ; width: 200px"></a>
</div>
<p>MIT OpenCourseWare By Prof.Andrew Sutherland</p>
<a href="https://ocw.mit.edu/courses/mathematics/18-785-number-theory-i-fall-2016/">
<button class="button" id="mit"><span>Visit </span></button>
</a>
</div>
</div>
</div>
<!-- END OF CONTENT -->
<!-- CUSTOM JS -->
<script src="js/prim.js"></script>
</body>
</html>