Dec. 2, 2022
\(\text{Find all } f : \mathbb{R} \rightarrow \mathbb{R} \text{ such that the following equality holds } \forall x,y \in \mathbb{R}: \) $$f(xy+1)=f(x)f(y)-f(y)-x+2.$$
Dec. 2, 2022
\(\text{Find all } f : \mathbb{R} \rightarrow \mathbb{R} \text{ such that the following equality holds } \forall x,y \in \mathbb{R}: \) $$f(xy)(x+f(y))=x^2f(y)+y^2f(x).$$
Nov. 10, 2022
\(\text{Find all } n \in \mathbb{N} \text{ such that } d \mid n \text{ and }\) $$dn + 1 \mid d^2 + n^2.$$
Nov. 10, 2022
\(\text{If } a, b, c \in \mathbb{R}_{> 0} \text{ such that } a + b + c \geqslant 1 \text{, prove following inequality:}\) $$\frac{a-bc}{a+bc} + \frac{b-ca}{b+ca} + \frac{c-ab}{c+ab} \leqslant \frac{3}{2}.$$
Nov. 4, 2022
\(\text{Find all values of } p, m, n \in \mathbb{N} \text{ such that } p \text{ is prime and }\) $$2^{m}p^{2} + 1 = n^{5}.$$