Solve Congruence Equations with Our Examples

Find the smallest positive integer k satisfying the stated condition or explain no such k exists:
$2^{k} \equiv 1 mod 14$ .

Tahmid Knox 2021-01-02

Solve the following linear congruences using Diophantine equations: $25 x \equiv 7 (mod 17) and 26 x \equiv 8 (mod 6)$

a2linetagadaW 2020-12-29

Determine whether the congruence is true or false.
$100 \equiv 20 m o d 8$

Tyra 2020-12-25

Determine the number of solutions of the congruence $x^{4} \equiv 61 (m o d 117)$

Cem Hayes 2020-12-24

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

CMIIh 2020-12-21

For each of the following congruences, find all integers N, with N>1, that make the congruence true.
$23 \equiv 13 (m o d N)$ .

lwfrgin 2020-12-16

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

remolatg 2020-12-13

For each of the following congruences, find all integers N, with N>1, that make the congruence true.
$6 \equiv 60 (m o d N)$ .

iohanetc 2020-12-09

For the triangles shown, we can express their congruence with the statement $△ A B C \tilde{=} △ F E D$ . By reordering the vertices, express this congruence with a different statement.

BenoguigoliB 2020-12-06

With of the following triangle congruence shortcuts could be used to prove PRQ = TRS

Given Data,
$∠ Q \tilde{=} ∠ S$
$\overset{―}{Q R} \tilde{=} \overset{―}{S R}$
a)Side-Side-Side Postulate (SSS)
b)Side-Angle-Side Postulate (SAS)
c)Angle-Side-Angle Postulate (ASA)
d)Angle-Angle-Side Theorem (AAS)

Chardonnay Felix 2020-12-03

Using the diagram below, complete the following congruence statement:
$△ A B C \tilde{=}$ ?

a) $△ D B C$
b) $△ B D C$
c) $△ B C D$
d) $△ D C B$

Cabiolab 2020-12-03

Write the set of solutions of
$x \equiv 5 (mod 24)$
$x \equiv 17 (mod 18)$

tabita57i 2020-11-27

Using Fermat's Little Theorem, solve the congruence $2 \cdot x^{425} + 4 \cdot x^{108} - 3 \cdot x^{2} + x - 4 \equiv 0 m o d 107$ .
Write your answer as a set of congruence classes modulo 107, such as {1,2,3}.

Bevan Mcdonald 2020-11-24

Find all whole number solutions of the congruence equation.
$(2 x + 1) \equiv 5 m o d 4$

Tahmid Knox 2020-11-12

Find the solution of the following system of congruences: (circ) 3x+4y= 1(mod11) 2x+5y= 7(mod11)

Dottie Parra 2020-11-12

Given the following system of linear simultaneous congruences what is the value of x that satisfies them all?
$x \equiv 18 mod 29$
$x \equiv 20 mod 31$
$x \equiv 6 mod 17$

Elleanor Mckenzie 2020-11-12

Write a two-column proof.
Given: $\overset{―}{M N} \tilde{=} \overset{―}{M P}, \overset{―}{N O} \tilde{=} \overset{―}{P O}$
Prove: $∠ N \tilde{=} ∠ P$

Emeli Hagan 2020-11-12

For the following statement, either prove that they are true or provide a counterexample:
Let a, b, m, $n \in Z$ such that m, n > 1 and $n ∣ m$ . If $a \equiv b (mod m)$ , then
$a \equiv b (mod n)$

Dillard 2020-11-09

Solve the congruence: $6 x \equiv 4 (m o d 10)$

illusiia 2020-11-08

Prove that the relation of congruence is an equivalence relation.

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