MathDB

5

Part of 2006 IMC

Problems(2)

IMC 2006, problem 5, day 1

Source: awful, doesn't say so much

7/22/2006
Let a,b,c,da, b, c, d three strictly positive real numbers such that a2+b2+c2=d2+e2,a^{2}+b^{2}+c^{2}=d^{2}+e^{2}, a4+b4+c4=d4+e4.a^{4}+b^{4}+c^{4}=d^{4}+e^{4}. Compare a3+b3+c3a^{3}+b^{3}+c^{3} with d3+e3,d^{3}+e^{3},
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IMC 2006, problem 5, day 2

Source:

7/25/2006
Show that there are an infinity of integer numbers m,nm,n, with gcd(m,n)=1gcd(m,n)=1 such that the equation (x+m)3=nx(x+m)^{3}=nx has 3 different integer sollutions.
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