integers

P and Q are two positive integers such that P² = Q² + 13. The product of the numbers P and Q is _________

It is given that x and y are integers in the following equation: $(x + y - 7)^2 + (y + 3x - 13)^2 = 0$ The value of $(x^3 + y^3)$ is ________ (in integer).

Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A x B x C), (B x G x E) and (D x E x F) are equal...

For non-negative integers, a, b, c, what would be the value of a + b + c if $$$\log \,a\, + \,\log \,b\, + \,\log \,c\, = \,0?$$$