MathDB

4

Part of 2022 Czech-Polish-Slovak Junior Match

Problems(2)

a/b - 1/2ab > \sqrt2 for pos.integers with a/b > \sqrt2

Source: 2022 Czech-Polish-Slovak Match Junior, individual p4 CPSJ

9/3/2022
Let aa and bb be positive integers with the property that ab>2\frac{a}{b} > \sqrt2. Prove that ab−12ab>2\frac{a}{b} - \frac{1}{2ab} > \sqrt2
inequalitiesnumber theory
diophantine systema, a + b = c , a^2 + b^3 = c^2

Source: 2022 Czech-Polish-Slovak Match Junior, team p4 CPSJ

9/3/2022
Find all triples (a,b,c)(a, b, c) of integers that satisfy the equations
a+b=c a + b = c and a2+b3=c2a^2 + b^3 = c^2
number theoryDiophantine equationDiophantine Equationsdiophantine