Maths WorkshopMaths problems with full solutions

Diophantine equations

10 problems · Diophantine equations.

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Ex.621x² + y² = 3z² has no non-trivial solution

#infinite descent #squares modulo 3 #Diophantine equations

Diophantine equations

Ex.622x² − y² = 2024

#Diophantine equations #factoring #parity #divisors

Diophantine equations

Ex.643When is 1! + 2! + … + n! a perfect square?

#squares modulo n #factorials #Diophantine

Diophantine equations

Ex.644Writing 1 as a sum of unit fractions

#Egyptian fractions #bounding #Diophantine

Diophantine equations

Ex.1338The Frobenius coin problem for two coins

#Frobenius number #linear Diophantine #Chicken McNugget

Diophantine equations

Ex.1340Infinitely many triangular numbers that are squares

#Pell equation #recurrence #infinitely many

Diophantine equations

Ex.1485Solving a linear Diophantine equation

#Diophantine equation #Bézout #particular solution

Diophantine equations

Ex.1486Solving $ax+by=c$

#Diophantine equation #Bézout #solvability criterion

Diophantine equations

Ex.1959When is n⁴ + n³ + n² + n + 1 a perfect square?

#bounding between squares #Diophantine equations

Diophantine equations

Ex.2233Vieta jumping: (a² + b²)/(ab + 1) is a square

#Vieta jumping #descent #Diophantine equations #extremal principle

Diophantine equations