Question

For how many unique coordinate points (p, q), such that p and q are integers, is it true that p2 - q2 = 1155?

Answer 1

Heya

◆ By Odd - Even Parity, one can say that, either both ( p + q ) and ( p - q ) are odd, or both are even but since the latter can't be possible, either 'p' or 'q' is even

Now, finding the solutions to :
${p}^{2} - {q}^{2} = 1155$

$= > (p + q)(p - q) = 1155$

Factors of 1155 : [ 1 x 3 x 5 x 7 x 11 ]

Number of factors that can be made from the above factors such that, ( p + q ) > ( p - q ) isn't repeated is : ( 5 + 3 )

0_0 The above can be determined by noting the factors in canonical form and calculating the π( k + 1 ) where 'k' represents the power of the factors.


But, along with the 8 in the first quadrant we can always count those in the third quadrant

And hence, there are ( 8 x 2 ) = 16 such unique points :v: