MathDB

39

Part of PEN H Problems

Problems(1)

H 39

Source:

5/25/2007
Let A,B,C,D,EA, B, C, D, E be integers, B≠0B \neq 0 and F=AD2−BCD+B2E≠0F=AD^{2}-BCD+B^{2}E \neq 0. Prove that the number NN of pairs of integers (x,y)(x, y) such that Ax2+Bxy+Cx+Dy+E=0,Ax^{2}+Bxy+Cx+Dy+E=0, satisfies N≤2d(∣F∣)N \le 2 d( \vert F \vert ), where d(n)d(n) denotes the number of positive divisors of positive integer nn.
quadraticsDiophantine Equations