Prove or disprove the following statement: ‘No cube of an integer has 2 as its units digit.’

This is a very standard proof question for the C3 exam. The first thing that I would do when I see wordy proof statements like this is to make sure I understand what it means. Maybe writing out the statement more simply might help. So for this statement: n^3 never ends in 2. The second thing is just to try a few examples. With this statement, the example you should start with are nice and clear:
1^3=1 2^3=8 3^3=27 4^3=64 5^3=125 So far we haven't seen a number ending in two, and we haven't seen a pattern with the final digits yet, so we must continue.  6^3=216 7^3=343 8^3=512 So by finding a number where the statement is not true, we have found a counter-example so we have disproved it.

TD
Answered by Thomas D. Maths tutor

6392 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the chain rule and how is it used?


Find the nature of the turning points of the graph given by the equation x^4 +(8/3)*x^3 -2x^2 -8x +177 (6 marks)


Differentiate y=x*ln(x^3-5)


Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning