AMC / AIME · Modular Arithmetic · Easy

Modular Arithmetic: How many integers math satisfy math?

Congruences and power cycles.

Try the problem

How many integers 1≤n≤501\le n\le 50 satisfy n≡2(mod5)n\equiv 2\pmod 5?

Hint and answer

Concept to use

$a\equiv b\pmod m$.

Hint

Arithmetic progression 2,7,12,…2,7,12,\ldots.

Answer

10

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