How about Gauss' Lemma? Gauss proved it in Disquisitiones Arithmeticae, the same work in which he developed modular arithmetic, but didn't use modular arithmetic to prove it. I once wrote a blog post about this, including his original proof and a modern one for comparison. (The blog post was intended for an audience of teachers so attempts to assume no abstract algebra background.)
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How about Gauss' Lemma? Gauss proved it in Disquisitiones Arithmeticae, the same work in which he developed modular arithmetic, but didn't use modular arithmetic to prove it. I once wrote a blog post about this, including his original proof and a modern one for comparison. (The blog post was intended for an audience of teachers so attempts to assume no abstract algebra background.) |
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