I think there is some mistake in the question as for h we're getting C=29

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a. p=5, q=13

n=p*q=65

$\Phi (n)$=(p-1)*(q-1)=48

d(private key) should be chosen such that d and $\Phi (n)$ have no common factors(they are relatively prime)

Possible choices for d=5,7,11,13,17

b. p=5, q=31 and d=37

n=p*q=155

$\Phi (n)$=(p-1)*(q-1)=120

the following relation must hold

e*d=1 MOD $\Phi (n)$

e*37=1 MOD 120

e*37 could be 121, 241, 361, 481 and so on

for here we obtain e=13

c. p=3, q=11, d=9

n=p*q=33

$\Phi (n)$=(p-1)*(q-1)=20

e*d=1 MOD $\Phi (n)$

e*9=1 MOD 20

e=9

for encryption $C=P^e MOD$ n

hello=8, 5, 12, 12, 15

h => $8^9 MOD$ 33=29

e => $5^9 MOD$ 33=20

l => $12^9 MOD$ 33=12

o => $15^9 MOD$ 33=3

n=p*q=65

$\Phi (n)$=(p-1)*(q-1)=48

d(private key) should be chosen such that d and $\Phi (n)$ have no common factors(they are relatively prime)

Possible choices for d=5,7,11,13,17

b. p=5, q=31 and d=37

n=p*q=155

$\Phi (n)$=(p-1)*(q-1)=120

the following relation must hold

e*d=1 MOD $\Phi (n)$

e*37=1 MOD 120

e*37 could be 121, 241, 361, 481 and so on

for here we obtain e=13

c. p=3, q=11, d=9

n=p*q=33

$\Phi (n)$=(p-1)*(q-1)=20

e*d=1 MOD $\Phi (n)$

e*9=1 MOD 20

e=9

for encryption $C=P^e MOD$ n

hello=8, 5, 12, 12, 15

h => $8^9 MOD$ 33=29

e => $5^9 MOD$ 33=20

l => $12^9 MOD$ 33=12

o => $15^9 MOD$ 33=3

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