How can we obtain $$\sum_{l=1}^{m}(-1)^{l+1} \binom{m}{l} \equiv 1 \pmod{p} $$
Please give me an idea to obtain this.
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not sure what you are asking exactly. for which values of $(m,p)$ the equality holds? – gt6989b Jan 21 '20 at 21:34
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6Idea: forget about $p$ and try to compute $$\sum_{l = 0}^{m} (-1)^l \binom{m}{l},.$$ – Daniel Fischer Jan 21 '20 at 21:36
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2expand $(1-1)^m=0$ using the binomial theorem – J. W. Tanner Jan 21 '20 at 21:42
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@J.W.Tanner Thank you so much! – Oily Jan 21 '20 at 22:58