Question

Prove that for all single digit prime numbers, p, p3 + p is a multiple of 10
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Answer 1

Step-by-step explanation:

(i) Prove that for all single digit prime numbers, P, p3 + p is a multiple of 10 (ii) Show, using algebra, that for n e N (n + 1)? – n' is not a multiple of 3

Answer 2

SOLUTION

TO DETERMINE

Prove that for all single digit prime numbers, p, p³ + p is a multiple of 10

EVALUATION

Here the given expression is p³ + p

Now all single digit prime numbers are 2 , 3 , 5 , 7

When p = 2 we have

p³ + p

= 2³ + 2

= 8 + 2

= 10 : which is a multiple of 10

When p = 3 we have

p³ + p

= 3³ + 3

= 27 + 3

= 30 : which is a multiple of 10

When p = 5 we have

p³ + p

= 5³ + 5

= 125 + 5

= 130 : which is a multiple of 10

When p = 7 we have

p³ + p

= 7³ + 7

= 343 + 7

= 350 : which is a multiple of 10

Hence proved

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