I am finding the remainder when $6^{88}$ is divided by $19$ , I applied Little theorem and obtained $9$, which is correct. My question is, can this be solved by using binomial theorem? I am not getting how to approach this.
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Refer to. https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference. For Mathjax tutorial – Rohan Shinde Jan 27 '18 at 18:37
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\begin{eqnarray} 6^{88} &=& 36^{44} \\ &=& (38-2)^{44}\\ &=& 38^{44}-44\cdot 38^{43}\cdot 2 + ...-44\cdot 38 \cdot 2^{43} +2^{44}\\ &=& 19a+2^{44} \end{eqnarray}
So you reduce your problem to $2^{44} = 16^{11} = (19-3)^{11} = 19b - 3^{11}$...
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sir wait iam posting mine answer , can you tell me how you are writing numbers like 6^8 where is option iam not finding it – Sumit Goyal Jan 27 '18 at 17:33
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yes i see but how to get that ?? menas how do i wru=ite myself what is option name – Sumit Goyal Jan 27 '18 at 17:36
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i wrote 6^88 and you write 6^88 neately which option is there to write numbers in power just like you write – Sumit Goyal Jan 27 '18 at 17:40
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