Prove that \( 2222^{5555}+5555^{2222} \) is divisible by 7 .

Channel:
PW Solutions
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=J4EUGZ3uSbA


Duration: 8:24
0 views
0

Prove that \( 2222^{5555}+5555^{2222} \) is divisible by 7 .
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03. If \( \sum_{r=0}^{2 n} a_{r}(x-2)^{r}=\sum_{r=0}^{2 n} b_{r}(x-3)^{r} \) and \( a_{k}=1 \) for...
2023-07-03If \( ^{n} J_{r_{r}}=\frac{\left(1-x^{n}\right)\left(1-x^{n-1}\right) \ldots\left(1-x^{n-r+1}\ri...
2023-07-03Show that \( \sum_{r=0}^{n} \frac{C_{r} \cdot 3^{r+4}}{(r+1)(r+2)(r+3)(r+4)} \) \[ -=\frac{1}{(n...
2023-07-03Prove that : \( { }^{\mathrm{n}} C_{0} \cdot{ }^{2 n} C_{n}-{ }^{n} C_{1} \cdot{ }^{2 n-2} C_{n}...
2023-07-03Find the sum of possible real Values of \( x \) for which the sixth term of the expansion of \( ...
2023-07-03Match the columns: \begin{tabular}{|c|l|l|l|} \hline \multicolumn{2}{|c|}{ Column-I } & \multico...
2023-07-03Find the number of divisors of the number \[ \mathrm{N}={ }^{2000} C_{1}+2 \cdot{ }^{2000} C_{2}...
2023-07-03Real value for \( x \) such that \( \sum_{k=0}^{4}\left(\frac{3^{4-k}}{(4-k) !}\right)\left(\fra...
2023-07-03Let \( \left(x^{3}+p x^{2}+2 x-5\right)^{19}\left(x^{2}+q x-41\right)^{8}\left(x^{4}-x^{3}+x-7\r...
2023-07-03Find the remainder when \( 32^{3232} \) is divided by 7 .
2023-07-03Prove that \( 2222^{5555}+5555^{2222} \) is divisible by 7 .
2023-07-03Prove that \( \sum_{m=0}^{n}{ }^{n} C_{m} \cdot \sin (m x) \cdot \cos (n-m) x=2^{n-1} \sin (n x) \)
2023-07-03Let \( N_{1}=2^{55}+1 \) and \( N_{2}=165 \). Then sum of digits of the HCF of \( N_{1} \) and \...
2023-07-03Match the columns: \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{ Column-I } & \multico...
2023-07-03Sum of the series \( S=\sum_{\mathrm{r}=0}^{\mathrm{n}} \frac{3^{\mathrm{r}+4}\left({ }^{\mathrm...
2023-07-03Let \( N=2^{1224}-1, \alpha=2^{153}+2^{77}+1 \) and \( \beta=2^{408}-2^{204}+1 \). Then which of...
2023-07-03Suppose \( [x] \) denote the greatest integer \( \leq \), and \( n \in N \), then \( \lim _{n \r...
2023-07-03The remainder when \( 2^{30} \cdot 3^{20} \) is divided by 7 is: (a) 1 (b) 2 (c) 4 (d) 6
2023-07-03The coefficient of \( x^{83} \) in \( \left(1+x+x^{2}+x^{3}+x^{4}\right)^{n}(x-1)^{n+3} \) is eq...
2023-07-03Suppose \( m \) and \( n \) are positive integers and let \( \mathrm{S}=\sum_{\mathrm{k}=0}^{\ma...
2023-07-03The value of \( \sum_{\substack{r=0}}^{s} \sum_{\substack{s=1 \\ r \leq s}}^{n} C_{s}^{s} C_{r} ...