What is the remainder,when 655^758 divided by 7?
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Given : 655⁷⁵⁸ Divided by 7
To Find : Remainder
Solution:
655⁷⁵⁸
= ( 93 * 7 + 4)⁷⁵⁸
Hence except 4⁷⁵⁸ all term are divisible by 7
4⁷⁵⁸
= 4⁷⁵⁶.4²
= ( 4³)252 * 16
= ( 64)²⁵² * 16
= (7 * 9 + 1)²⁵² * (2* 7 + 2)
remainder 1 * remainder 2
= remainder 2
Hence remainder = 2
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