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Prove the following theorem: for all integers a, b and c, if a does not divide b - c

then a does not divide b or a does not divide c. Hint: an indirect proof would work

well.

Prove that there do not exist two positive integers x and y such that x^2 - 4y^2 = 14.

Additional information: you have all known for a long time that there are many

solutions to the equation x^2 + y^2 = z^2, where x, y and z are all positive integers.

This problem considers a slightly dierent, but similar looking, type of equations.

Hint: use an indirect proof, and start by factoring x^2 - 4y^2.

I don't fully understand how to write a proper proof. Thanks for anyone's help!