A number theory problem by Priyanshu Mishra

Number Theory Level 3

Four positive integers x , y , z , x, y, z, and t t satisfy the relations

x y − z t = x + y = z + t . \large\ xy - zt = x + y = z + t.

Is it possible that both x y xy and z t zt are perfect squares?

Sometimes Yes and Sometimes No Yes No Not perfect squares, but perfect cubes.

Priyanshu Mishra by Priyanshu Mishra , 20, India

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