Find the smallest positive integer N such that N/2 is a perfect
cube, N/3 is a perfect fifth power and N/5 is a perfect seventh
Stage: 4 Challenge Level:
This problem is a good one with which to illustrate the precision of meaning that mathematics often requires - in this case the precedence of the operations.
Superficially the task provides some practice at interpreting negative indices but more deeply it invites students to find a simplification for the 'stacked' indices.
The real variable each time is the value, of the four, which is selected as base. To explore that students might go on to consider which sets of four values will produce the same 'stacked' value, irrespective of stacking order.
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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.