Finding all a for a=frac{62k+1}{k-1}

[Patronas]

$$a=\frac{62k+1}{k-1}$$
or
a = [62k+1] / [k-1]

a, k are natural numbers
I must find all a

 

[dacruick]

what do you mean you must find all a. Through what method must you find all a?

 

[mathman]

For starters k must be even. If k is odd, k - 1 is even and 62k + 1 is odd.

 

[Patronas]

I know that k must be even. But then, I calculate for k=2, k=4, k=6 ... And I have results a=63, 65, 69, 71, 83, 125 but i need good method

 

[mathman]

k-1 must divide evenly into 63. k=2,4,8,10,22.