Q) Find the remainder of 37^47^57 divided by 16?

Any help will be appreciated?

Thanks,

Ashish

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- Oct 26th 2009, 03:31 AMa69356Remainder?
Q) Find the remainder of 37^47^57 divided by 16?

Any help will be appreciated?

Thanks,

Ashish - Oct 26th 2009, 11:49 AMSoroban
Hello, Ashsh!

I*think*I've solved it . . .

Quote:

Find the remainder of divided by 16

. . we have: .

Now consider consecutive powers-of-5 (mod 16):

. .

The remainders step through a 4-step cycle: .

Now we must determine: .

We have: .

Hence: .

And: . has remainder 13.

Therefore: .

But someone check my reasoning and work ...*please!*

.