Library / /189 of 520
Number theory Difficulty 5.9 AIME, harder Prove it
16. Prove: The system of indeterminate equations x2+y2=z2,x2−y2=w2 has no positive integer solutions.
Solution
16. Use Theorem 2 to derive a contradiction.
Want a route through all this instead of an archive?
The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic and difficulty added by this site.