Algebraic Reasoning & Proof (Higher)

Interactive macro-enabled MS-Excel spreadsheet. Contents: Prove (n ± a)² − (n ± b)² is a multiple of a № for integer values of n. Prove (kn ± c)² ± (kn ± c) is a multiple of a № for integer values of n. Prove (an ± b)² ± (cn ± d)² is a multiple of a № for integer values of n. Prove the difference between the squares of two №s is their sum. Prove the difference between squares of terms is a multiple of a №. Prove the difference between the mean of squares & the mean² is ¼. Prove the sum of friends’ ages sharing a birthday is a multiple of 3. Prove the product of a № & the one following/preceding × ½ is n². Prove the last digit of any square number never equals 2, 3, 7 or 8. Prove the sum of first ten terms of a Fibonacci sequence is 11 × u₇. Prove the square of any odd number is 1 more than a multiple of 8. Prove the sum of the four rules for the faces of a painted cube is n³. Prove the sides of two non-similar right-angled triangles are related.