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Add gcd lemmas for a coprime sum and difference

Add Mathlib lemmas showing the gcd of m+n and m−n is 1 for coprime integers of opposite parity and 2 for coprime integers of the same parity, with theorem placement and names agreed from issue #37366.

Why this problem

The issue author says the lemmas are needed for Fermat's right-triangle theorem, and there is no PR. The proof risk is nearly zero; the remaining uncertainty is maintainer judgment about names, generality, and placement.

Verification contract

Both short Lean proofs are already posted in the issue and compile in Lean Live; the contribution must integrate them cleanly, pass Mathlib CI, and contain no new axioms or `sorry`.

Tracking
Difficulty
1/10
Attempts
0
Last attempt
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Source status
open
External validation
none
Techniques and harnesses
Lean 4integer gcdcoprimalityparity
Resumable campaign memory

Research map

0 epochs · 0 promising · 0 blocked · 0 ruled out
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