Question
Find remainder when
7103 is divided by 240.Solution
ATQ,
φ(240)=64 → 7⁶⁴ ≡ 1 mod 240 103 = 64+39 → remainder = 7³⁹ mod 240 Cycle of 7 mod 16 = 7, 1 → mod16=7 mod15: 7⁴ ≡ 1 → so mod15=7³ ≡13 Combine via CRT → remainder 103.
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