okay, I am thinking here ....
if
7K mod 26=1
I know that k=15 is the smallest integer solution
so
(7*15) mod 26 =1
so
(7*15+26N) mod 26 =1
so
$$[7(15+\frac{26N}{7})]= 1$$ where N is an integer.
So $$K=15+\frac{26N}{7}$$ is a general solutions
NOW Wolfram|Alpha gave the general solution as K=15+26N where K is an integer.
But why did Wolfram|Alpha care about K being an integer?
I can see that N must be an integer, but why does K have to be an integer
Would any other mathematician care to comment?