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Found: 3

Problem #PRU-31304

Problems Number Theory Number theory. Divisibility Equations in integer numbers

Solve the equation with natural numbers $1 + x + x^{2} + x^{3} = 2 y$ .

Problem #PRU-30395

Problems Number Theory Number theory. Divisibility Equations in integer numbers

Prove there are no natural numbers $a$ and $b$ , such as $a^{2} - 3 b^{2} = 8$ .

Problem #PRU-31287

Problems Number Theory Number theory. Divisibility Equations in integer numbers

Prove there are no integer solutions for the equation $x^{2} + 1990 = y^{2}$ .