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{{nowrap|''p<sup>n</sup>'' / ''q<sup>n</sup>'' {{=}} ''m''}}, and {{nowrap|''p<sup>n''</sup> {{=}} ''mq<sup>n''</sup>}}. This means ''p'' is divisible by ''m''. Therefore, there exists some integer ''r'' such that {{nowrap|''p'' {{=}} ''mr''}}, so we now have {{nowrap|''m<sup>n</sup>r<sup>n</sup>'' {{=}} ''mq<sup>n</sup>''}}. Dividing both sides by ''m'' gives{{nowrap|''m''<sup>{{nowrap|''n'' − 1}}</sup>''r<sup>n''</sup> {{=}} ''q<sup>n</sup>''}}. This means that ''q'' must also be divisible by ''m'', which is a contradiction, since ''p'' and ''q'' were assumed to be relatively prime. | {{nowrap|''p<sup>n</sup>'' / ''q<sup>n</sup>'' {{=}} ''m''}}, and {{nowrap|''p<sup>n''</sup> {{=}} ''mq<sup>n''</sup>}}. This means ''p'' is divisible by ''m''. Therefore, there exists some integer ''r'' such that {{nowrap|''p'' {{=}} ''mr''}}, so we now have {{nowrap|''m<sup>n</sup>r<sup>n</sup>'' {{=}} ''mq<sup>n</sup>''}}. Dividing both sides by ''m'' gives{{nowrap|''m''<sup>{{nowrap|''n'' − 1}}</sup>''r<sup>n''</sup> {{=}} ''q<sup>n</sup>''}}. This means that ''q'' must also be divisible by ''m'', which is a contradiction, since ''p'' and ''q'' were assumed to be relatively prime. | ||
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{{escape notice}} | {{escape notice}} | ||