Question

2. Prove that there is no integer 𝑛 such that 7|4𝑛^2−3
3. Find the remainder by division by 7 of 99999999.
4. Find the remainder in the division by 17 of 15!
5. Let 𝑝 be a prime. Show that for all integer𝑎𝑎 we have that 𝑝|𝑎𝑝+(𝑝−1)!𝑎 and 𝑝|𝑎+(𝑝−1)!𝑎𝑝.