<p>I have a doubt in one question for isi</p><p>it is question number 21 of subjective of tomato book.</p><p>for a natural number n,let an=n^2+20. If dn denotes the greatest common divisor of an and a(n+1) then show dn divides 81</p>
<p>let n=1</p><p>therefore an = 1^2 + 20 = 21</p><p> an+1 = 2^2 + 20 = 24</p><p>dn = 3 and it divides 81</p><p>now, let n =2</p><p>therefore an = 24</p><p> an+1 =29</p><p>dn = 1 and it divides 81</p><p>similarly it will hold true for other cases as well</p>
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