(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.

2 x t divided by n

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answer: 5

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hello,

b) 62.47% of the students are between 14 and 18 years old.

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mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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