• 대한수학회보
• /
• 제52권4호
• /
• pp.1133-1138
• /
• 2015

In 1956, $Je{\acute{s}}manowicz$ conjectured that, for any positive integer n and any primitive Pythagorean triple (a, b, c) with $a^2+b^2=c^2$, the equation $(an)^x+(bn)^y=(cn)^z$ has the unique solution (x, y, z) = (2, 2, 2). In this paper, under some conditions, we prove the conjecture for the primitive Pythagorean triples $(a,\;b,\;c)=(4k^2-1,\;4k,\;4k^2+1)$.