03-18-2015, 08:45 AM

Time out extended for above puzzle.

Meanwhile here's the new one. The solution is a relatively long one, but I'd encourage you to jog your memory cells.

Tip: You will need to know a little 'modular arithmetic'. The rest is just simple logic. Try using a paper and pen / pencil.

'Square Sum'

Find all pairs of positive integers (m, n), satisfying the following equation.

where, 2^x refers to '2 raised to the power of the number x'.

PS: I didn't solve it myself. I looked up the solution right away :-p

Meanwhile here's the new one. The solution is a relatively long one, but I'd encourage you to jog your memory cells.

Tip: You will need to know a little 'modular arithmetic'. The rest is just simple logic. Try using a paper and pen / pencil.

'Square Sum'

Find all pairs of positive integers (m, n), satisfying the following equation.

2^2016 + 2^2012 + 2^2008 + 2^m = n^2 .

where, 2^x refers to '2 raised to the power of the number x'.

PS: I didn't solve it myself. I looked up the solution right away :-p

(This post was last modified: 03-18-2015, 08:46 AM by radiobox.)

Progress might have been all right once, but it has gone on too long -- Ogden Nash