Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
In y = ax +b when are a, -b/a, b in arithmetic progression. The
polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2
and c be in arithmetic progression?
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1,
2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a
- b) = ab.
Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6.
Find some examples of three primes which include the number 3 and form an AP, and show that in every such case the common difference is not divisible by 6.