MathDB

4

Part of 2020 JBMO TST of France

Problems(2)

Number Theory with sequences

Source: First JBMO TST of France 2020, Problem 4

3/4/2020
Let a0,a1,...a_0, a_1,... be a sequence of non-negative integers and b0,b1,...b_0, b_1,... be a sequence of non-negative integers defined by the following rule: bi=gcd(ai,ai+1)b_i=gcd(a_i, a_{i+1}) for every i=>0i=>0 Is it possible every positive integer to occur exactly once in the sequence b0,b1,...b_0, b_1,...
number theory
Inequality

Source: France JBMO TST 2020 Test 2 P4

3/11/2020
a,b,ca, b, c are real positive numbers for which a+b+c=3a+b+c=3. Prove that a12+b12+c12+8(ab+bc+ca)≥27a^{12}+b^{12}+c^{12}+8(ab+bc+ca) \geq 27
inequalitiesalgebraFranceJBMO TST