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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
- calculus - Exponential Decay Question: The Half-Life of Cesium-137 is . . .
Exponential Decay Question: The Half-Life of Cesium-137 is 30 Years Suppose We Have a 100-mg Sample Ask Question Asked 10 years, 4 months ago Modified 10 years, 4 months ago
- A tetrahedron for 2025 - Mathematics Stack Exchange
Joe Malkevitch suggested exploring tetrahedra with edge lengths $3,3,3,3,5,5$, in light of $3^4 \\cdot 5^2 = 2025$ Q Is this realization unique? I e , is there no other incongruent tetrahedron with
- Making a polygon using equilateral triangles and squares.
Does the newly formed convex polygon have to be “filled in completely” using the squares and triangles? Or should the squares and triangles just be “on the perimeter” of the polygon?
- The longest distance travelled by an ant on the sides of a cube.
That seems incomplete as an answer The problem is not that you enter a vertex twice - that is allowed by the question The problem is that if there are only three edges to any vertex, then you cannot enter and leave a vertex twice without tracing one of the three edges twice I think that is an essential element of the solution that needs to be stated expliclity
- geometry - Draw an isosceles triangle equal in area to a triangle ABC . . .
I am trying to solve the question Draw an isosceles triangle equal in area to a triangle ABC, and having its vertical angle equal to the angle A I have tried to approach the problem from backward
- Cubic matrix equation - Mathematics Stack Exchange
Cite edited Feb 24 at 15:21 Oscar Lanzi 51 3k 2 56 137 answered Feb 24 at 13:17 Dietrich Burde 143k 8 100 182
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