Abstract :
The author shows that (1) for any m set membership, variant image, the equation xm + ym = zm has a solution in SL2image if and only if m is not divisible by 3 or 4; (2) for any A set membership, variant Mnimage and any integer p, there are x, y set membership, variant Mnimage such that x + Y = A and det X = (−1)n · det Y = p; (3) for any A set membership, variant Mnimage and any integer p, if n greater-or-equal, slanted 3 is odd, then there are x, y, z set membership, variant Mnimage such that x + y + Z = A and det x = det Y = det Z = p.
