Q−3: [5×4 marks]
a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7.
b. Write the prime factorization of 229320 and 49140, hence find
GCD and LCM.
c. Convert the following number (1303)4 to base 5.
d. Using the Prime Factorization technique determine whether 173 is
a prime.
e. Use the cipher: f(x)=(x+7) mod 26 to decrypt “THAO ALZA”.
let p = 1031, Find the number of solutions to the equation x^2
-2 y^2=1 (mod p), i.e., the number of elements (x,y),
x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)