MATH 4109 Modules 16-19 2025/2026
Exam Questions and Answers | 100%
Solved
What are Mersenne primes? - 🧠ANSWER ✔✔prime numbers that can be
written in the form 2^n - 1
Which of the following is known as Euler's identity? - 🧠ANSWER ✔✔e^(ix)
= cos x + i(sin x)
What do we call two numbers that are equal to the sum of the proper
divisors of the other number? - 🧠ANSWER ✔✔Friendly numbers
Euler gave several proofs of Heron's formula for the area of a triangle with
side lengths a, b, and c.: Area=sqrt(s(s−a)(s−b)(s−c))
What is s? - 🧠ANSWER ✔✔Half the perimeter of the triangle
Are there any odd perfect numbers? - 🧠ANSWER ✔✔This remains an
unsolved problem.
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, Which number did Euler refer to as "neither nothing, nor greater than
nothing, nor less than nothing"? - 🧠ANSWER ✔✔sqrt(-1)
With which physical disability was Euler afflicted in his later years? -
🧠ANSWER ✔✔He was blind.
Euler's work on the Konigsberg Bridge Problem laid the foundations for
which branch of mathematics? - 🧠ANSWER ✔✔Graph Theory
What are the three points that lie on an Euler line? - 🧠ANSWER
✔✔Centroid, Circumcenter, Orthocenter
Why is Leonhard Euler known as the most prolific mathematician? -
🧠ANSWER ✔✔He wrote a massive amount of material during his lifetime,
much of which remained unpublished at his death.
What is the restriction on the function, f(x), in the Fundamental Theorem of
Calculus? - 🧠ANSWER ✔✔f(x) must be continuous on [a,b]
How did Newton's Generalized Binomial Theorem improve on the
expansion of (a+b)^n - 🧠ANSWER ✔✔n could be any rational number
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY
STATEMENT. ALL RIGHTS RESERVED
2
Exam Questions and Answers | 100%
Solved
What are Mersenne primes? - 🧠ANSWER ✔✔prime numbers that can be
written in the form 2^n - 1
Which of the following is known as Euler's identity? - 🧠ANSWER ✔✔e^(ix)
= cos x + i(sin x)
What do we call two numbers that are equal to the sum of the proper
divisors of the other number? - 🧠ANSWER ✔✔Friendly numbers
Euler gave several proofs of Heron's formula for the area of a triangle with
side lengths a, b, and c.: Area=sqrt(s(s−a)(s−b)(s−c))
What is s? - 🧠ANSWER ✔✔Half the perimeter of the triangle
Are there any odd perfect numbers? - 🧠ANSWER ✔✔This remains an
unsolved problem.
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY
STATEMENT. ALL RIGHTS RESERVED
1
, Which number did Euler refer to as "neither nothing, nor greater than
nothing, nor less than nothing"? - 🧠ANSWER ✔✔sqrt(-1)
With which physical disability was Euler afflicted in his later years? -
🧠ANSWER ✔✔He was blind.
Euler's work on the Konigsberg Bridge Problem laid the foundations for
which branch of mathematics? - 🧠ANSWER ✔✔Graph Theory
What are the three points that lie on an Euler line? - 🧠ANSWER
✔✔Centroid, Circumcenter, Orthocenter
Why is Leonhard Euler known as the most prolific mathematician? -
🧠ANSWER ✔✔He wrote a massive amount of material during his lifetime,
much of which remained unpublished at his death.
What is the restriction on the function, f(x), in the Fundamental Theorem of
Calculus? - 🧠ANSWER ✔✔f(x) must be continuous on [a,b]
How did Newton's Generalized Binomial Theorem improve on the
expansion of (a+b)^n - 🧠ANSWER ✔✔n could be any rational number
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY
STATEMENT. ALL RIGHTS RESERVED
2
