A huge division

Number Theory Level 2

N = 560560560560563. N=560560560560563. Sharky divided N 2 N^2 by 8 8 . He will get a remainder:

3 3 1 1 7 7 4 4

Aaryan Maheshwari by Aaryan Maheshwari , 16, India

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2 solutions

Kenny O.
Sep 14, 2017

N= 8n +3 where n = 70070070070070.
( 8 n + 3 ) 2 = 64 n 2 + 16 n + 9 (8n+3)^2=64n^2+16n+9 , as 64 n 2 + 16 n 64n^2+16n is already divisible by 8, we do not need to care about them.
9 divided by 8 has a remainder of 1.

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Aaryan Maheshwari
Sep 11, 2017

We just need to find the last 3 3 digits of N 2 N^2 , which are 969 969 . When 969 969 is divided by 8 8 , the remainder is 1 1 .

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