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prove that every positive integer different from 1 can be expressed as a product of non negative power of 2 and an odd no



prove that every positive integer different from 1 can be expressed as a product of non negative power of 2 and an odd no 



Grade:10

1 Answers

sanatan sharma
26 Points
12 years ago

let n be a positive integer different from 1 

then it can be expressed as : n= p1a1p2a2p3a3......pkak

there can be 2 different possibilities

1)-    when p1 = 2 and  p1a1p2a2p3a3......pkak are odd positive integers

        n= 2a1 x  ( p1a1p2a2p3a3...... pkak )

        n = ( a non- negative power of 2) x (an odd positive integer)

2)-   whem each of p1a1p2a2p3a3......pkak are odd positive integers

       n = p1a1p2a2p3a3......pkak

       n = 20 x p1a1p2a2p3a3......pkak

       n =  ( a non- negative power of 2) x (an odd positive integer)

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