paul Monsky
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 80 Have any long-suspected irrational numbers turned out to be rational? 36 An example of a beautiful proof that would be accessible at the high school level? 15 Is there an elementary way to find the integer solutions to $x^2-y^3=1$? 14 Not especially famous, long-open problems which anyone can understand 14 What are some correct results discovered with incorrect (or no) proofs?

### Reputation (2,812)

 +20 Is there an elementary way to find the integer solutions to $x^2-y^3=1$? +5 Dissecting trapezoids into triangles of equal area +5 If p is a prime congruent to 9 mod 16, can 4 divide the class number of Q(p^(1/4))? +5 Does this variant of a theorem of Hasse (really due to Gauss) have an “elementary” proof?

### Questions (29)

 17 Does this variant of a theorem of Hasse (really due to Gauss) have an “elementary” proof? 16 If p is a prime congruent to 9 mod 16, can 4 divide the class number of Q(p^(1/4))? 15 Higher level analogs of Nicolas-Serre theory 14 The “Level N modular equation for delta” in characteristics 3, 5, 7 and 13 12 Simple groups with the same cardinality as PSL_2(Z/p)

### Tags (51)

 81 nt.number-theory × 41 21 algebraic-number-theory × 4 29 diophantine-equations × 3 18 ag.algebraic-geometry × 9 27 co.combinatorics × 8 15 elementary-proofs 25 quadratic-forms × 10 14 characteristic-p × 27 22 modular-forms × 32 12 binomial-coefficients

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