From the blog
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The Diophantine equation X⁴-Y⁴-X=0
Let’s solve the Diophantine equation X⁴-Y⁴-X=0 together so as to see a standard approach that is encountered in solving Diophantine equations of the form Z(f(Z)-1)=Y²…
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A simple Diophantine equation
Let’s solve a Diophantine equation together using only elementary considerations. Suppose we are asked to determine all the integers X and Y such that X³-X+1=3Y⁵.…
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Valore esatto di cos(2π/5)
Exercise for high school students who have studied complexes and are wondering what they can be used for. Let’s show that cos(2π/5)=(-1+√5)/4. (1) Let w=cos(2π/5)+isin(2π/5)…
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Complex roots
Given a complex w and a positive natural number n, we say that z is the nth root of w if zⁿ=w. We set: ⁿ√w…
Marco Damele 