Question

show that any positive integer is of the form 4q+1 as 4q+3 where Q is some integer

Answer 1

let a be an any positive integer where b= 4...
By Euclid Algorithm a = 4q +r
such that q >_ 0...r = 0,1,2,3 because 0<_ r < 4
a = 4q , 4q+1 , 4q +2, 4q+3

if a = 4q , 4q +2...so it is an even...so by euclid...odd and even can also positive integer....By this,
4q + 1 , 4q + 3 is an positive integer.

HENCE PROVED
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#Hope its help you#..

Answer 2

hey

here is answer

let a be any positive integer

then

b= 4

a= bq+r

0≤r<b

0≤r<4

r= 0,1,2,3

case 1.

r=0

a= bq+r

4q+0

4q

case 2.

r=1

a= 4q+1

6q+1

case3.

r=2

a=4q+2

case 4.

r=3

a=4q+3

hence from above it is proved that any positive integer is of the form 4q, 4q+1,4q+2,4q+3


hope it helps

thanks