- #1
physics kiddy
- 135
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Question is :
If m,k,n are natural numbers and n>1, prove that we cannot have m(m+1)=kn.
My attempt :
Using induction:
If m follows this rule... m+1 must follow it ..
so
(m+1)(m+2) = kn
Since every natural number can be expressed as the product of primes, it follows that (m+1) and (m+2) are primes.
Now, my question is...
are there any two consecutive primes which can be expressed in the form of kn.
Thanks for any help.
If m,k,n are natural numbers and n>1, prove that we cannot have m(m+1)=kn.
My attempt :
Using induction:
If m follows this rule... m+1 must follow it ..
so
(m+1)(m+2) = kn
Since every natural number can be expressed as the product of primes, it follows that (m+1) and (m+2) are primes.
Now, my question is...
are there any two consecutive primes which can be expressed in the form of kn.
Thanks for any help.
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