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shubhamsrg Group Title

Show that if p and p + 2 with p ≥ 5, are both primes then the number p + 1 is always divisible by 6.

  • 2 years ago
  • 2 years ago

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  1. shubhamsrg Group Title
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    p and p+2 are surely odd,, thus p+1 is even --> hence p+1 is always divisible by 2. we now need to prove p+1 is also divisible by 3..am stuck there..

    • 2 years ago
  2. mathslover Group Title
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    p + 1 is even right?

    • 2 years ago
  3. shubhamsrg Group Title
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    yep..

    • 2 years ago
  4. mathslover Group Title
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    hmn wait

    • 2 years ago
  5. shubhamsrg Group Title
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    yes..maybe even i made a breakthrough,,i shall just post something..

    • 2 years ago
  6. Herp_Derp Group Title
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    p is either equivalent to 1 mod 3 or 2 mod 3. then p+2 is the other one. So p+1 must be 0 mod 3

    • 2 years ago
  7. shubhamsrg Group Title
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    exactly what i was going to post.. :D

    • 2 years ago
  8. shubhamsrg Group Title
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    thank you buddies :)

    • 2 years ago
  9. mathslover Group Title
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    :) welcome though I didn't help

    • 2 years ago
  10. shubhamsrg Group Title
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    well you gave my question time..thats not a small thing! ;)

    • 2 years ago
  11. mathslover Group Title
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    You made me feel proud haha

    • 2 years ago
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