Question

If 2^200-2^192×31+2ⁿ is a perfect square then n=?

Answer 1

2^200-2^192 ×31+2^n
=2^192(2^8-31+2(n-192))
=2^192(256-31+2^k) {let k = n-192}
=2^192(225+2^k)
2^192 is a perfect square. Choose k such that 225+2^k will also become a perfect square. By trial k = from 1 to 5 no one satisfy this requirment. But k= 6 can satisfy it.
(225+2^6=289 is perfect)
k= 6
So, 6=n-192
n=192+6
n=198

Answer 2

Answer:

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