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hsbhatt

Fermat's Little Theorem says 6¹⁰ = 11k+1

Hence 6³³⁰ is of the form 11k+1

6⁸ = (33+3)⁴

Hence remainder when 6⁸ is divided by 11 is same as when 3⁴ = 81 is divided by 11, which is 4. Hence 6⁸ is of the form 11k+4

Thus 6³³⁸ = 6³³⁰ 6⁸ is of the form 11k+4.

Hence 6³³⁸ leaves remainder 4 on division by 11.

@jeesucks, u can read abt Fermat's theorem in any standard text or on the net. But do look it up

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