Prove that the square of an odd number is always 1 more than a multiple of 4
An odd number can be expressed by the formula "2n + 1" where n stands for any integer. Therefore, the square of any odd number can be expressed as:(2n+1)^2 = (2n+1)(2n+1) = 4n^2 + 4n + 1 = 4(n^2 + n) + 1As 4(n^2 + n) is necessarily a multiple of 4, it is therefore clear that 4(n^2 + n) + 1 is 1 more than a multiple of four. Therefore the square of any odd number is 1 more than a multiple of 4
EB
Related Maths GCSE answers
All answers ▸One of the teachers at a school is chosen at random. The probability that this teacher is female is 3/5. There are 36 male teachers at the school. Work out the total number of teachers at the school.
f(x) = x^2 + 4x − 6 f(x) can be written in the form (x + m)^2 + n. Find the value of m and the value of n.
Solve the simultaneous equations 5x + 2y = 4 and x - y - 5 =0
2(y+3) = 10. What is y?