Prove: If N Is an Integer That Is Not a Multiple

question 68

Short Answer

Prove: if n is an integer that is not a multiple of 4, $$\text { then } n ^ { 2 } \equiv 0 \bmod 4 \text { or } n ^ { 2 } \equiv 1 \bmod 4 \text {. }$$

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Definitions:

Zero-Coupon Bond

A bond that does not pay periodic interest, but is issued at a deep discount, with the return being the difference between the purchase price and the face value at maturity.

Stripped Bond

A debt security where the principal and regular coupon payments have been separated and are sold as individual securities.

Inflation Premium

The part of the nominal interest rate that represents compensation to the lender for the loss of purchasing power due to inflation.

Fisher Effect

An economic theory stating that the real interest rate is independent of monetary measures, especially the nominal interest rate and the expected inflation rate.