AMC / AIME · Modular Arithmetic · Medium

Modular Arithmetic: How many integers math are coprime to math?

Congruences and power cycles.

Try the problem

How many integers 1≤n≤1051\le n\le 105 are coprime to 105105?

Hint and answer

Concept to use

Units digits / cycles.

Hint

φ(105)=φ(3)φ(5)φ(7)\varphi(105)=\varphi(3)\varphi(5)\varphi(7).

Answer

48

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