Middle school
A power repeats multiplication; positive integers start at one.
3² means 3 × 3. Change the shared exponent on 3, 4 and 5: when does the sum of the first two equal the third?
Exponent 2: left 25, right 25.
These are examples for one triple, not a proof for every positive integer triple.
Compare the numbers in the question with the diagram you are moving. You can try again.
Set the exponent to 2: the equality holds. Now notice the condition n≥3. A counterexample must satisfy the hypotheses too.
Your answer fits this explanation. Look for the same idea in the comic.
No; exponent 2 is outside that claim. Set the exponent to 2: the equality holds. Now notice the condition n≥3. A counterexample must satisfy the hypotheses too.
3² + 4² = 9 + 16 = 25 = 5². The condition 3 ≤ n excludes this example.
FLT · aa2d8b3 · S_fermat_last_theorem.lean
theorem solution (n : ℕ) (hn : 3 ≤ n) (a b c : ℕ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ n + b ^ n ≠ c ^ n :=FLT.fermatLastTheorem n hn a b c ha.ne' hb.ne' hc.ne'
In the signature, hn is the exponent condition; ha, hb and hc require positive bases. The symbol ^ denotes a power.
Powers and positive integers
Read the three explanation steps first. The Lean source is there for a closer look afterwards; you do not have to read it first.
A power repeats multiplication; positive integers start at one.
Earlier ideas are listed under “Start with these ideas” on this page.
3² + 4² = 9 + 16 = 25 = 5². The condition 3 ≤ n excludes this example.
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