Bunuel wrote:
If n and y are positive integers and n represents the number of different positive factors of y, is y a perfect square?
(1) √n is an odd integer
(2)\( y =\sqrt{5^{2(n-1)}}\)
n,y: positive integers
n = f(y)
if y is a perf square, then n=odd
ie. y=25, f(25)=5ˆ2=(2+1)=3
ie. y=16,f(16)=2ˆ4=(4+1)=5
(1) √n is an oddinteger sufic
if √n=odd, (n positive integer), then n=oddˆ2 which is an oddnumber
(2)\( y =\sqrt{5^{2(n-1)}}\) insufic
\( y =\sqrt{5^{2(n-1)}}=5ˆ(n-1)\)
n=1: 5ˆ0=1 perfsquare=yes
n=2: 5ˆ(2-1)=5perfsquare=no
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