# Knowing what Excel can do for you

Algebra Level 4

If $$f (x) = x^7 - p x^6 + q x^5 - r x^4 + s x^3 - t x^2 + u x - 5027$$ such that:

$$f (1) = 1$$

$$f (2) = 1$$

$$f (3) = 2$$

$$f (4) = 3$$

$$f (5) = 5$$

$$f (6) = 8$$

$$f (7) = 13$$

Given that $$p, q, r, s, t$$ and $$u$$ are positive rational numbers,

then $$find$$ the $$sum$$ of $$denominators$$ of $$p, q, r, s, t$$ and $$u$$,

where all of them are $$'false'$$ fractions of numerator > denominator,

which have been simplified with GCD (numerator, denominator) = 1.

GCD: Greatest Common Divisor (for positive integers), for example GCD (24, 10) = 2. $$False$$ $$fraction$$ is an expression commonly used by Chinese communities.

Inspired by original question set by Dev Sharma.

×