If we divide 5^2500 by 7, which remainder of following remainders do w

Question

If we divide 5^2500 by 7, which remainder of following remainders do we get?

A. 0
B. 1
C. 2
D. 3
E. 4

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beeblebrox · Answer

Have used Fermat's theorem to solve the question. Refer attached.

RanonBanerjee · Answer

5 has cyclicity of (5,5,5,0). 2500 is divisible by 4. So the last digit of 5^2500 would be 0.

Any number with zero as last digit, if divided by 7 gives reminder 3.

So ans is D.

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AveeshSingroha · Answer

5^2500 = 625^625

625 divided by 7 gives the remainder 2

So, 625^625 for our sake can be written as 2^625
2^625 = (2^5)^125 = 32^125

32 gives a remainder 4 when divided by 7
So,
now we have 
4^125 = 1024^25
1024 gives a remainder 2 when divided by 7

So,
we have,
2^25 = 32^5
32 gives a remainder 4 when divided by 7

so we have 4^5 = 1024 and this gives a remainder of 2 when divided by 7

bumpbot · Answer

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If we divide 5^2500 by 7, which remainder of following remainders do w

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GMAT Problem Solving (PS) Questions

If we divide 5^2500 by 7, which remainder of following remainders do w

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