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MR1765981 11D45 (11B68 11D41)
Brindza, B.; Pintér, Á. On the number of solutions of the equation $1\sp k+2\sp k+\cdots+(x-1)\sp k=y\sp z$. Dedicated to Professor Kálmán Győry on the occasion of his 60th birthday. Publ. Math. Debrecen 56 (2000), no. 3-4, 271–277.
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