43 citations · 84 across the 15 of their papers we have counts for
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math.NT2010
Reducing the Erdos-Moser equation 1^n + 2^n + . . . + k^n = (k+1)^n modulo k and k^2
Jonathan Sondow, Kieren MacMillan
An open conjecture of Erdos and Moser is that the only solution of the Diophantine equation in the title is the trivial solution 1+2=3. Reducing the equation modulo k and k^2, we g…
math.NT2010
Proofs of power sum and binomial coefficient congruences via Pascal's identity
Kieren MacMillan, Jonathan Sondow
A frequently cited theorem says that for n > 0 and prime p, the sum of the first p n-th powers is congruent to -1 modulo p if p-1 divides n, and to 0 otherwise. We survey the main…
math.NT2010★ 5 cited
Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental
Diego Marques, Jonathan Sondow
We give a brief history of transcendental number theory, including Schanuel's conjecture (S). Assuming (S), we prove that if z and w are complex numbers, not 0 or 1, with z^w and w…