sauravshakya
j^3 = 61 + i^6
Find all the integer solution of i and j.



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sauravshakya
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One is i=2 and j=5

sauravshakya
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What about other?

Jonask
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\[j^3(i^2)^3=61\]
\[(ji^2)(j^2+ij+i^2)=61\]
61 is prime so 61(1) are the only factors
hence \[ji^2=1,j^2+ij+i^2=61\]

sauravshakya
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Looks like 4 solution.

Jonask
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but we imgore the fact that it can be vise versa 1(61)

sauravshakya
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dw:1350668697206:dw

Jonask
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oh thanks i see my folly i did not factor 2


sauravshakya
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Looks like 2 and 5 only.......... But how to prove it mathematically.

Jonask
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\[i^4+2i^2+1+i^2(1+i^2)+i^4=61\]
\[3i^4+3i^260=0,i^4+i^210=0\]

Jonask
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sorry
\[i^4+i^220\]

Jonask
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yes

Zekarias
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ok

Jonask
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\[i=\pm 2,j=(\pm2)^2+1=5\]

Zekarias
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@Jonask you are very correct

sauravshakya
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Looks good.