Number Theory/Expert Profile

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Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience in the area

Teacher of math for 53 years


AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley


Journal of mathematics and its applications M500 magazine


BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors

State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients

I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

What do you like about this subject?

The variety, and the fact that everyone can participate. Anyone could discover a new largest prime number by joining the Mersenne prime project, using their computer off-line in the background to do masses of calculations.

What do you still hope to achieve/learn in this field?

I would love to have enough knowledge to completely understand Andrew Wiles's proof of Fermat's last theorem.

Something interesting about this subject that others may not know:

Secure encrypted messaging can be dependent on the difficulty of factorising the product of two large prime numbers.

Something controversial or provocative about this subject

Does the beauty I find in number theory demand a divine creator for the Universe?

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    K = Knowledgeability    C = Clarity of Response    P = Politeness
Kenneth10/01/16101010Thanks for the great reply! Yes, it .....
Gregory09/27/1610Thank you for your time.
Prashant S Akerkar 08/15/16101010Dear Prof Vijilant Thanks. Prashant
Prashant S Akerkar 07/30/16101010Dear Prof Vijilant Thanks. Prashant

Recent Answers from Vijilant

2016-09-30 Rates: Follow-Up:

Hello Kenneth  The amount of work done, w, is proportional to the number of men, m,  the hours per day, h, and the number of days.  So w = kmhd  substituting gives w = k*24*8*15 = 2880k  Now the same w

2016-08-23 Rates:

I think I have been over this with you before.  The number of houses is jointly proportional to the number of men and the number of days.  So h = kmd.  Substituting the given gets you to k = 1/40.  So

2016-08-15 Plotting graphs in 2nd,3rd & 4th quadrant.:

Hello Prashant  Clearly, a straight line graph cannot be in all four quadrants, but a graph of Fahrenheit against Celsius is in 1st,2nd and 3rd.  A bar graph showing the profits or losses of a firm in

2016-08-07 Help:

I'm not sure if I understand the question, but I think you mean 24 hour clock time.  All times from noon to 1 minute to midnight have 12 hours added, so that confusion between 10 am and 10 pm does not

2016-07-25 Two candidates having same number of votes.:

Hello Prashant  We need to know the number of votes cast. Suppose there are two candidates and 2v votes are made.  Assume candidate A can receive any number of votes from 0 to 2v with equal probability


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