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Prove that, 36^7−6^13 is divisible by 30.

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take out the HCF
36^7−6^13
= 6^14 - 6^13
= 6^13(6-1)
= 5(6^13)
clearly 6^13 is divisible by 6
and 5(6^13) is divisible by 5, so
5(6^13) is divisible by 5*6 or 30

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