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sedikit modif

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tentukan semua tripel bilangan bulat ganjil berurutan
(a, b, c) sedemikian sehingga a^2 + b^2 + c^2 merupakan bilangan dg 5 digit yg semua digitnya sama.

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$a=n-1$

$b=n$

$c=n+1$

maka $a^2+b^2+c^2=3n^2+2$

 

5 digit sama = kkkkk 

kalau dikurangi 2 jadi 

kkkk(k-2) kongruen 5k-2 = 2k-2 mod 3

atau 

(k-1)(k-1)(k-1)(k-1)(k+8) kongkuen (5k+4) = 2k +1 mod 3

 

dua opsi ini tidak ada yang merupakan kelipatan 3 (agar jadi $3n^2$. jadi tidak ada solusi

 

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