Find the \(1001^{st}\) term in

\(2^2-1^2=3\)

\(3^2-2^2=5\)

\(4^2-3^2=7\)

\(3^2-1^2=8\)

\(5^2-4^2=9\)

\(⋮\)

Geven that a is an odd number, show that \(\left(a^2-1\right)\) is a multiple of 8.

The oattern for the sum of consecutive even numbers befinning from 2 is as follows:

 \(2=2=1\times2\)

\(2+4=6=2\times3\)

\(2+4+6=12=3\times4\)

\(2+4+6+8=20=4\times5\)

\(2+4+6+8+10=30=5\times6\)

\(⋮\)

Devise an expression for the sum of n consecutive even numbers.

Express 123476543 as a product of two consecutive odd numbers.

It is given that (a + b + c) is an add number. Show that (a + b + c) \(\times\)(a - b + c) is also an odd number.

It is given \(\dfrac{ab}{a+b}=8\). The value of (a+b) is a square number. Find a and b.

Given abc = \(n^2\) and \(a\times b\times c=n+3\). Find the 3-digit number.

Geven \(abc=n^2\) and \(a\times b\times c=n+3\). Find the 3-digit number.

Given 36a + 252b is a square number, where a and b are positive integers.

Find the least value of a+b.

It is given \(ab+ba=n^2\), where n is a positive integer. Find the positive values of a and b.