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Problem #PRU-60389

Problems Algebra Algebraic equations and systems of equations Binomial theorem

How many rational terms are contained in the expansion of

a) $(\sqrt{2} + \sqrt[4]{3})^{100}$ ;

b) $(\sqrt{2} + \sqrt[3]{3})^{300}$ ?

Problem #PRU-100320

Problems Algebra Algebraic equations and systems of equations

Show that $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1$ is not solvable in natural numbers.

Problem #PRU-30416

Problems Algebra Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property

The board has the form of a cross, which is obtained if corner boxes of a square board of $4 \times 4$ are erased. Is it possible to go around it with the help of the knight chess piece and return to the original cell, having visited all the cells exactly once?