jessie
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Friday 14 August 2026 13:05:36 GMT
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∫ ∑(S∀UL)dx πθλ 🇮🇹™️ :
This was my friend’s interview question for Oxford Maths!
2026-08-14 13:11:41
15
Next Person :
Let X=∏pᵢᵃⁱ, Y=∏pᵢᵇⁱ. From X^c=Y^d we get aᵢc=bᵢd, so bᵢ/aᵢ=c/d=R. Thus Y=X^R. Then X^(X^R)=(X^R)^X ⇒ X^R=RX ⇒ X^(R−1)=R ⇒ X=R^(1/(R−1)). Let X1. f(R)=R^(1/(R−1)) is strictly decreasing for R>1, with lim(R→1+)f(R)=e1, the only possible value is X=2, giving R=2 and Y=4. So the only solutions are (2,4) and (4,2).
2026-08-14 15:35:05
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