It is given \(3\times5=15=4^2-1\)
\(5\times7=35=6^2-1\)
\(7\times9=63=8^2-1\)
\(9\times11=99=10^2-1\)
\(⋮\)
Write a formula for the number parttern.
Find a value of n, such that \(2^6+2^9+2^n\)is a square number.
Two numbers are relatively prime if their only common factor is 1. How mayny numbers less than 50 are relatively prime to 50 ?
How many factors does the number 300 have?
How many ways are there to write 37 as the sum of at least three prime numbers ?
It is given 7m +n = mn +11 = prime, where m and n are both prime too.
Find \(m^2+n^2\).
Determine if the follwing numbers are prime:
(a) 1997
(b) 123456789
(c) (23456719)
ITs is given a+b=3 and a.b = 4.Find the value of \(a^2+b^2\).
Find the value of m and n, for which they satisfy \(m^2-n^2=64\)
Compute:
\(\left(123456\right)^2-123457\times123455\)
Expand the following:
(a) \(\left(2x+3\right)^2\)
(b) \(\left(x-2\right)^3\)
a,b,c and d satisfy a system of equations:
\(\left\{{}\begin{matrix}2a+b+c+d=15\\a+2b+c+d=30\\a+b+2c+d=5\\a+b+c+2d=0\end{matrix}\right.\)
Find value 6a+4b
Solve for the values of r,s,t and u in the follwing equations:
\(\left\{{}\begin{matrix}2r+s=4\\2t+u=10\\2s+t=7\\2u+r=9\end{matrix}\right.\)