# Problems Section: Problems 1291 - 1300

Q1291 Show that there do not exist three primes $x$, $y$ and $z$ satisfying $$x^2 + y^3 = z^4$$.

Q1292 Prove that for all $a$, $b$, $c$, and $d$ satisfying $0 \le a, b,c,d \le 1$, there holds $$\frac{a}{b+c+d+1} + \frac{b}{c+d+a+1} + \frac{c}{d+a+b+1} + \frac{d}{a+b+c+1} + (1-a)(1-b)(1-c)(1-d) \le 1.$$