(5) non-linear diophantine equations (5 marks) (a) let p be a prime such that p = 2,3 mod 5. prove the diophantine equation: x^2 – 5y² =p has no integer solutions. (b) find primes of the form p = 0,1,4 mod 5 (one for each congruence class) for which there are solutions to the equation in part a) and give a solution in each case.

the first one

step-by-step explanation:

just id the test.

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v