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For any positive integer n, prove that n cube -n is divisible by 6

Posted by Pooja Arora 6 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Tinku Munda 6 years, 9 months ago

According to euclid division lemma any positive integer is of the form 6m, 6m+1, 6m+2, 6m+3, 6m+4, 6m+5. If a=6m (a)³= (6m)³ =216m³ =6(36m) =6n ( n=36m) If a=6m+1 (a)³=(6m+1) =(6m)³ + 3*(6m)² * (1) +3 *(6m) * (1)² + (1)³ =216m³ + 108m² + 18m + 1 =6(36m³ + 18m² + 3m) + 1 =6n+1 (n=36m³ + 18m² + 3m) + 1 Similarly you have to find if you can't than tell me latter ok baby

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