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

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

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
What about other?
 2 years 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 \[ji^2=1,j^2+ij+i^2=61\]
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Looks like 4 solution.
 2 years 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)
 2 years ago

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

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

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

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

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

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

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

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