List questions from congruences

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Number of unique congruence classes with a specific property

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If $x^5 ≡ 2 $(mod $17$) then $x ≡ 15 $(mod $17$)

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Identity involving pentagonal numbers

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Using linear congruence to solve a further equation

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Find integer $x$ such that -2310 ≤ $x$ ≤ 2310...

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Solve the conditional congruence 371x ≡ 287 (mod 460)....

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There is a general and his army of 13 soldiers (14 people in total) raided an enemy base...

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Show that if $a\equiv b\pmod m$ and $c\equiv d\pmod m$, then $ac\equiv bd\pmod m$

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If $\gcd(m,n) = 1$, show that $m^{φ(n)} + n^{φ(m)} ≡ 1 \mod{mn}$

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Solve $40x + 13\equiv 78 \pmod {105}$.

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Find the measure of a side and an angle.

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Is Congruence Class an example of Equivalence Class? (Understanding the definition through Examples)

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List Question

2009 Benelux Math Olympiad (BxMO) number theory problem

Number of unique congruence classes with a specific property

Solving higher congruence

If $x^5 ≡ 2 $(mod $17$) then $x ≡ 15 $(mod $17$)

Identity involving pentagonal numbers

Using linear congruence to solve a further equation

Find integer $x$ such that -2310 ≤ $x$ ≤ 2310...

Solve the conditional congruence 371x ≡ 287 (mod 460)....

There is a general and his army of 13 soldiers (14 people in total) raided an enemy base...

Show that if $a\equiv b\pmod m$ and $c\equiv d\pmod m$, then $ac\equiv bd\pmod m$

If $\gcd(m,n) = 1$, show that $m^{φ(n)} + n^{φ(m)} ≡ 1 \mod{mn}$

Solve $40x + 13\equiv 78 \pmod {105}$.

Find the measure of a side and an angle.

Is Congruence Class an example of Equivalence Class? (Understanding the definition through Examples)

Proving modular arithmatic congruence

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