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We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a result, we get additional information on the possible sizes of Tate-Shafarevich groups of the associated elliptic curves.
We also present a related criterion for primes p such that divides the class number of the imaginary quadratic field ℚ(√-p)....
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