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sauravshakya
Group Title
j^3 = 61 + i^6
Find all the integer solution of i and j.
 one year ago
 one year ago
sauravshakya Group Title
j^3 = 61 + i^6 Find all the integer solution of i and j.
 one year ago
 one year ago

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sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
One is i=2 and j=5
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
What about other?
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
\[j^3(i^2)^3=61\] \[(ji^2)(j^2+ij+i^2)=61\] 61 is prime so 61(1) are the only factors hence \[ji^2=1,j^2+ij+i^2=61\]
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Looks like 4 solution.
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
but we imgore the fact that it can be vise versa 1(61)
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
dw:1350668697206:dw
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
oh thanks i see my folly i did not factor 2
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=All+integer+solution+x^3+%3D+61+%2B+y^6
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Looks like 2 and 5 only.......... But how to prove it mathematically.
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
\[i^4+2i^2+1+i^2(1+i^2)+i^4=61\] \[3i^4+3i^260=0,i^4+i^210=0\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
sorry \[i^4+i^220\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.2
\[i=\pm 2,j=(\pm2)^2+1=5\]
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.0
@Jonask you are very correct
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Looks good.
 one year ago
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