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Properties of The Number 137 - Mathematics Stack Exchange There are some other Properties for $137$ in Wikipedia I found another Properties such that $137=2^7+2^3+1$ or the only way to write the number $137$ as a summation of two square numbers is $137=4^2+11^2$ thanks for your advice and suggestions Edit: After reading comments and answers, I want to suggest a definition for such numbers like $137$
Find an integer $r$ with $0 ≤ r ≤ 10$ such that $7^ {137 }≡ r (\text . . . Your working is fine You need to end by noting that $-5 \equiv 6 \pmod {11}$ since they asked for a residue between $0$ and $10$ An alternative approach would be: $7^ {137} \equiv (-4)^ {137} \equiv -2^ {274} \equiv - (2^ {5})^ {54} \cdot 2^4 \equiv - (32)^ {54} \cdot 16 \equiv - (-1)^ {54} \cdot 16 \equiv - 16 \equiv -5 \equiv 6 \pmod {11}$ I prefer this approach to reduce the base in
Upper and lower bounds - Mathematics Stack Exchange By halving 5 (the number you are rounding to) = 2 5 Then to find the upper bound you add it to the number you are rounding so 135 + 2 5 = 137 5 ( this is a multiple of 5)