Question

a number can be squared ,show that this number is of the form

Answer 1

\[\large\color{green}{4k\text{ or } 4k+1}\]

Answer 2

hence or otherwise show that if an interger is both a sqaure and a cube it can be written as \[\large\color{blue}{7k\text{ or }7k+1 }\]

Answer 3

@ParthKohli

Answer 4

basic number theory -elementary!!!

Answer 5

Suppose that the number (say \(n\)) is even.\[n = 2x \Rightarrow n^2 = 4x^2 \Rightarrow n^2 = 4k \tag{if x^2 = k}\]Continue with \(n\) as even

Answer 6

Let's see how I go about the second one... hmm

Answer 7

okay good start then what about the other form

Answer 8

hint same trick

Answer 9

\(n\) as odd*

Answer 10

\[n = 2k + 1 \Rightarrow n^2 = 4k^2 + 4k + 1 \Rightarrow n^2 = 2(2k^2 + 2k) + 1\]:-P

Answer 11

Whoops\[n^2 = 4(k^2 + k) + 1\]