Fermat's last theorem?
Does there exists integers a , b and c such that a 1 0 0 + b 1 0 0 = c 1 0 0 ?
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2 solutions
Let a = 0 , b = 0 , c = 0 then 0 1 0 0 + 0 1 0 0 = 0 1 0 0
Urgh, that title mislead me. Forgot the case of 0.
Oh God, I totally forgot that 0 is also an integer!
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Exactly, i feel guilty of getting this one wrong
Don't you mean: a = b = c = 0 ? @Zakir Husain
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Yes, but it is also true if either a = 0 or b = 0
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I don't think so. This will only be true when all a , b , c are = 0 . If either of them are non-zero, the equation has no solution
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@Mahdi Raza – No, if a = 0, a 1 0 0 + b 1 0 0 = c 1 0 0 is true for all b = c
@Mahdi Raza – if a = 0 then b = ± c will be a solution, and if b = 0 then a = ± c will be a solution see below 0 1 0 0 + b 1 0 0 = b 1 0 0 a 1 0 0 + 0 1 0 0 = a 1 0 0
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@Zakir Husain – It will also be b = − c at a = 0 and a = − c at b = 0
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@Aryan Sanghi – LaTeX, please! @Aryan Sanghi
@Aryan Sanghi – Sure, why not?
@Aryan Sanghi – Well pointed out. Because the power of 100 is even here, if it were to be odd, it will not have been true. Am I right?
@Zakir Husain – Got it, thank you!
@Zakir Husain , nice question. Took me off guard!
(a=b,c=0),(a=c,b=0),(b=c,a=0)