yadavneetu75488 yadavneetu75488
  • 14-06-2017
  • Mathematics
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prove that the square of any positive integer is of the 3m or 3m+1 but not of the form 3m+2

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ghanami
ghanami ghanami
  • 14-06-2017
hello : 
prove : n²≡0 (mod 3) or n²≡1 (mod 3)...no    n²≡2 (mod 3)
1 ) n ≡ 0 (mod 3)....(1)
     n² 
≡  0 (mod 3)
2) n ≡ 1 (mod 3)....(2)
     n² ≡ 1 (mod 3)
3 ) n ≡ 2 (mod 3)....(3)
     n² ≡ 4 (mod 3)  but : 4≡ 1 (mod 3) 
so :  n² ≡ 1 (mod 3)
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