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

This Question is Closed

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

Jonask
 3 years ago
Best 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 \[ji^2=1,j^2+ij+i^2=61\]

sauravshakya
 3 years ago
Best ResponseYou've already chosen the best response.1Looks like 4 solution.

Jonask
 3 years ago
Best ResponseYou've already chosen the best response.2but we imgore the fact that it can be vise versa 1(61)

sauravshakya
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1350668697206:dw

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

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

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

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

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

Zekarias
 3 years ago
Best ResponseYou've already chosen the best response.0@Jonask you are very correct
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