show that any positive odd number is of the form 6q+1, 6q+1, 6q+5. where q is some integer
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Answered by
2
hey dear
here is your answer
Let a is positive odd integer which when divided by 6 gives q and quotient and r as remainder
using Euclid division lemma
a = bq + r
where a = 0, 1 ,2 ,3 ,4 ,5
then
a= 6q
a = 6q +1
a = 6q +2
a= 6q + 3
a = 6q + 4
a = 6q +5
here we see that ( 6q + 1 , 6q + 3 , 6q +5 )
these are odd integer
hence shown
_________________________________
hope it helps
thank you
here is your answer
Let a is positive odd integer which when divided by 6 gives q and quotient and r as remainder
using Euclid division lemma
a = bq + r
where a = 0, 1 ,2 ,3 ,4 ,5
then
a= 6q
a = 6q +1
a = 6q +2
a= 6q + 3
a = 6q + 4
a = 6q +5
here we see that ( 6q + 1 , 6q + 3 , 6q +5 )
these are odd integer
hence shown
_________________________________
hope it helps
thank you
TISHUVERMA25:
THANKS BRO...
Answered by
0
Answer:
Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder.
according to Euclid’s division lemma
a=bq+r
a=6q+r
where , a=0,1,2,3,4,5
then,
a=6q
or
a=6q+1
or
a=6q+2
or
a=6q+3
or
a=6q+4
or
a=6q+5
but here,
a=6q+1 & a=6q+3 & a=6q+5 are odd.
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