TAOCP 3.2.1.1: Choice of Modulus
Section 3.2.1.1 exercises: 14 solved.
Section 3.2.1.1. Choice of Modulus
Exercises from TAOCP Volume 2 Section 3.2.1.1: 14 solved.
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TAOCP 3.2.1.1 Exercise 1
Let $w$ denote the machine word size of MIX.
TAOCP 3.2.1.1 Exercise 2
We are asked to write a MIX subroutine that computes the next value of a linear congruential sequence.
TAOCP 3.2.1.1 Exercise 3
Let P=ax, with
TAOCP 3.2.1.1 Exercise 4
**Exercise 3.
TAOCP 3.2.1.1 Exercise 5
Since $0 \le x,y<m$, we have $-(m-1)\le x-y\le m-1.$ Hence $(x-y)\bmod m$ is either $x-y$ or $x-y+m$.
TAOCP 3.2.1.1 Exercise 6
Consider the recurrence X_{n+1} \equiv aX_n-c \pmod m.
TAOCP 3.2.1.1 Exercise 7
Examination of Table 1 reveals several recurring structural patterns in the factorizations of $w \pm 1$.
TAOCP 3.2.1.1 Exercise 8
We are asked to write a MIX program analogous to program (2) of Section 3.
TAOCP 3.2.1.1 Exercise 9
Let q=\left\lfloor \frac{m}{a}\right\rfloor , \qquad r=m\bmod a,
TAOCP 3.2.1.1 Exercise 10
Let m=aq+r,\qquad q=\left\lfloor \frac{m}{a}\right\rfloor,\qquad 0\le r<a.
TAOCP 3.2.1.1 Exercise 11
Let T_a(x)=ax \bmod m , where $0<a<m$.
TAOCP 3.2.1.1 Exercise 12
Let M=9999999999=10^{10}-1.