MathDB

1

Part of 1993 China Team Selection Test

Problems(2)

find the value of f(p)

Source: China TST 1993, problem 1

6/27/2005
For all primes p≥3,p \geq 3, define F(p)=∑k=1p−12k120F(p) = \sum^{\frac{p-1}{2}}_{k=1}k^{120} and f(p)=12−{F(p)p}f(p) = \frac{1}{2} - \left\{ \frac{F(p)}{p} \right\}, where {x}=x−[x],\{x\} = x - [x], find the value of f(p).f(p).
modular arithmeticnumber theory unsolvednumber theory
2 * x^4 + 1 = y^2

Source: China TST 1993, problem 4

6/27/2005
Find all integer solutions to 2x4+1=y2.2 x^4 + 1 = y^2.
modular arithmeticnumber theorygreatest common divisornumber theory unsolved