Solve Congruence Equations with Our Examples

Prove the transitivity of modular congruence. That is, prove that for all integers a,b,c, and n with n > 1, if $a = b (m o d n) a n d b = c (m o d n) t h e n a = c (m o d n)$ .

Jason Farmer 2021-01-31

Find the least positive integer n that satisfies the congruence
$7^{128}$ congruent to n (mod13)

Albarellak 2021-01-31

Find the smallest positive integer solution to the following system of congruences:
$x \equiv 17 (mod 35)$
$x \equiv 8 (mod 43)$

hexacordoK 2021-01-30

In congruence classes $\frac{Z}{m Z}$ , reduce the equation $a_{m} \cdot x_{m}^{2} = c_{m}$ either by finding convenient representation for $a_{m} and b_{m}$ or by using the inverse of $a_{m}$ . Then find a solution for this congruence directly or by replacing $c_{m}$ : with its appropriate representative in $\frac{Z}{m Z}$ . If there is no solution explain why. Here $a_{m}, b_{m}, x_{m} (= x), c_{m} \in \frac{Z}{m Z} :$
$I n \frac{Z}{19 Z}, [2] \cdot x^{2} = [13] :$

alesterp 2021-01-28

Find the smallest positive integer k satisfying the stated condition or explain no such k exists:
$3^{k} \equiv 1 mod 11$ .

Lewis Harvey 2021-01-28

Find the smallest positive integer k satisfying the stated condition or explain no such k exists:
$2^{k} \equiv 1 mod 11$ .

generals336 2021-01-24

Solve the following linear congruence: 17x congruence 3(mod 7)

Yasmin 2021-01-19

Determine whether the congruence is true or false.
$7 \equiv 21 m o d 3$

bobbie71G 2021-01-19

Determine whether the congruence is true or false.
$88 \equiv 5 m o d 9$

Caelan 2021-01-19

In the roof truss shown, AB = 8 and $m ∠ H A F = 37^{\circ}$ . Find: $m ∠ B A D$ .
(HINT: The design of the roof truss displays line symmetry.)

amanf 2021-01-17

Label each of the following statements as either true or false.
The distinct congruence classes for congruence modulo n form a partition of Z.

Carol Gates 2021-01-17

Solve the congruence $x^{20} - 1 \equiv 0 (m o d 61)$

djeljenike 2021-01-13

Solve the following linea congruence: 17x congruence 3(mod 210)

abondantQ 2021-01-13

Find the smallest positive integer x that solves the congruence:
$7 x \equiv 5 (mod 52)$

sodni3 2021-01-13

Consider the system of linear congruences below:
$x \equiv 2 (mod 5)$
$2 x \equiv 22 (mod 8)$
$3 x \equiv 12 (mod 21)$
(i)Determine two different systems of linear congruences for which the Chinese Remainder Theorem can be used and which will give at least two of these solutions.

aflacatn 2021-01-10

Using the given premise, identify the third congruence necessary to demonstrate the congruence of triangles

a) $\overset{―}{O M} \tilde{=} \overset{―}{T S}$
b) $∠ M \tilde{=} ∠ S$
c) $\overset{―}{O N} \tilde{=} \overset{―}{T R}$
d) $∠ O \tilde{=} ∠ T$

hexacordoK 2021-01-10

Does congruence of triangles have the reflexive property? the symmetric property? the transitive property?

Dillard 2021-01-06

Solve the congruence $x^{20} - 1 \equiv 0 (mod 61)$

arenceabigns 2021-01-06

Determine whether the congruence is true or false.
$88 \equiv 5 m o d 9$ .

OlmekinjP 2021-01-04

Prove directly from the definition of congruence modulo n that if a,c, and n are integers, $n > 1$ , and $a \equiv c (mod n), t h e n a^{3} \equiv c^{3} (mod n)$ .

Those high school students who had a difficult time with their Geometry studies might remember the pains of solving a congruence equation. If you have to do it for your design or Architecture course, you should not worry because we have the list of questions that have been posted by students like you along with the answers to help you see how this aspect of Geometry works.

It only seems complex upon the surface, yet once you get some practice and find solutions like the ones listed below, you will be able to implement Geometry skills for your course.

Congruence Examples for High School