Binomial expansion in ring

Reference no: EM13126547

Let p be a prime. Show that in the ring Z-p (set of integers modulo p) we have (a+b)^p = a^p+b^p for all a, b in Z-p. The following hint was given: observe that the usual binomial expansion for (a+b)^n is valid in a commutative ring.

Reference no: EM13126547

Questions Cloud

Find probability less than eight which distribution have : Among 200 randomly selected dvd of this type suppose u have to find the probability x is less than 8 which distribution does this have?

Determine ideals and rings-homomorphisms : Prove the Second Isomorphism Theorem: If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S, respectively, and (S+A)/A isomorphic to A/(S intersecting A).

What is the ksp of the mf2 : Some MF2 is dissolved in water at 25oC to make a saturated solution. (M is a mystery metal - it's identity can be ignored.) Some of the solution is removed and tested

Total cost recovery deduction : Audra elects section 179 for asset C. Audra's taxable income from her business would not create a limitation for purposes of the section 179 deduction. Audra elects not to take additional first-year depreciation. Determine her total cost recovery ..

Binomial expansion in ring : Let p be a prime. Show that in the ring Z-p (set of integers modulo p) we have (a+b)^p = a^p+b^p for all a, b in Z-p. The following hint was given:

What was the standard deviation and mean sales : That 95% of all daily sales fell between $19,200 and $36,400. Based on this information what were the mean sales? What was the standard deviation?

Calculate the percent of the acid : if the freezing point of a .106 m CH3COOH solution is -.348 degrees Celsius, calculate the percent of the acid that has undergone ionization?

Net method of accounting for purchase discounts : Assuming Hydra uses the perpetual inventory system and the net method of accounting for purchase discounts, what amount is recorded as inventory from this purchase?

What is the molarity of the sulfuric acid : If the density of the solution is 1.1094 g/mL, what is the molarity of the sulfuric acid?

User Account

All Pages