Show that any positive even integer in the for m of4q or 4q+1, where q is an integer
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hey !!
here ,the pb goes like this....
let us start taking with a,where a is a positive odd integer.
we apply euclids division algorithm with a and b=4.
since 0≤r∠4 ,the possible remainders are 0,1,2,and 3....
that is , a can be 4q, or 4q+1 or 4q+2 , or 4q+3 ,where q is the quotient.
however, since a is odd , a cannot be 4q or 4q+2 (since they both r divisible by 2).
∴ any odd integer is a the form 4q+1 or 4q+3
hope my ans helps u.....^-^
here ,the pb goes like this....
let us start taking with a,where a is a positive odd integer.
we apply euclids division algorithm with a and b=4.
since 0≤r∠4 ,the possible remainders are 0,1,2,and 3....
that is , a can be 4q, or 4q+1 or 4q+2 , or 4q+3 ,where q is the quotient.
however, since a is odd , a cannot be 4q or 4q+2 (since they both r divisible by 2).
∴ any odd integer is a the form 4q+1 or 4q+3
hope my ans helps u.....^-^
shuzu:
hope my sol. helps u :) ^-^
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