N is a positive integer such that each of 3*N + 1 and 4*N + 1 is a perfect square.
Is N always divisible by 56?
If so, prove it. Otherwise, give a counterexample.
It looks like yes, n=56 creates 169 and 225 ,both perfect squares.
Evaluating members manually of two series a1=3*m*56+1 and a2=4*m*56+1 ,I did not find any m number causing a perfect square number in both series.
That is not a proof ,but unless a counterexample is found I
believe that N=56 might be the only case and therefore the following statvement is true:
If N is a positive integer such that each of 3*N + 1 and 4*N + 1 is a perfect square-than N is divisible by 56.
...still waiting for more cases or counterexample...
Edited on April 2, 2010, 4:36 am
starting with one sample
