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Show that an integer of the form 6k+5 is also of the form 3k+2, but not conversely
 2 years ago
 2 years ago
Show that an integer of the form 6k+5 is also of the form 3k+2, but not conversely
 2 years ago
 2 years ago

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2bornot2bBest ResponseYou've already chosen the best response.0
I think I can work on the first part, but have no idea on the second "converse part'
 2 years ago

Mani_JhaBest ResponseYou've already chosen the best response.1
Can you show your work on the first part?
 2 years ago

2bornot2bBest ResponseYou've already chosen the best response.0
So if an integer is of the form 6k+5, then it is equivalent to 6k+3+2, which is equal to 3(2k+1)+2. Now if k is an integer 2k+1 is also an integer, so it is of the form 3k+2
 2 years ago

2bornot2bBest ResponseYou've already chosen the best response.0
I am sorry, I should have mentioned k is an integer.
 2 years ago

Mani_JhaBest ResponseYou've already chosen the best response.1
Yes, then just try the reverse. 3k+2=6k+53k3 =6k3(k+1)+5 6{k(k+1)/2}+5 =6(k1)/2+5 (k1)/2 may not be an integer if n is even. See that the expression does not come out to be in the form 6n+5, where n is an integer. So the converse is true sometimes, but not always.
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.0
for the converse...just give a specific counter example
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.0
2=3*0+2 2=6k+5 3=6k k=1/2 which is not an integer
 2 years ago
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