tmua 2019 Q4

tmua · Uk · paper2 1 marks Proof True/False Justification

Consider the following conjecture:
If $N$ is a positive integer that consists of the digit 1 followed by an odd number of 0 digits and then a final digit 1 , then $N$ is a prime number.
Here are three numbers:
I $\quad N = 101$ (which is a prime number)
II $\quad N = 1001$ (which equals $7 \times 11 \times 13$ )
III $N = 10001$ (which equals $73 \times 137$ )
Which of these provide(s) a counterexample to the conjecture?

..... 6

Consider the following conjecture:

If $N$ is a positive integer that consists of the digit 1 followed by an odd number of 0 digits and then a final digit 1 , then $N$ is a prime number.

Here are three numbers:

I $\quad N = 101$ (which is a prime number)

II $\quad N = 1001$ (which equals $7 \times 11 \times 13$ )

III $N = 10001$ (which equals $73 \times 137$ )

Which of these provide(s) a counterexample to the conjecture?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20