Current Progress
Much work has been done classifying congruent numbers.
For example, it is known that if p is a prime number then
- if p ≡ 3 (mod 8), then p is not a congruent number, but 2p is a congruent number.
- if p ≡ 5 (mod 8), then p is a congruent number.
- if p ≡ 7 (mod 8), then p and 2p are congruent numbers.
Read more about this topic: Congruent Number
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